1 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.]
57 /* ====================================================================
58 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
67 * 2. Redistributions in binary form must reproduce the above copyright
68 * notice, this list of conditions and the following disclaimer in
69 * the documentation and/or other materials provided with the
72 * 3. All advertising materials mentioning features or use of this
73 * software must display the following acknowledgment:
74 * "This product includes software developed by the OpenSSL Project
75 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78 * endorse or promote products derived from this software without
79 * prior written permission. For written permission, please contact
80 * openssl-core@openssl.org.
82 * 5. Products derived from this software may not be called "OpenSSL"
83 * nor may "OpenSSL" appear in their names without prior written
84 * permission of the OpenSSL Project.
86 * 6. Redistributions of any form whatsoever must retain the following
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
95 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102 * OF THE POSSIBILITY OF SUCH DAMAGE.
103 * ====================================================================
105 * This product includes cryptographic software written by Eric Young
106 * (eay@cryptsoft.com). This product includes software written by Tim
107 * Hudson (tjh@cryptsoft.com).
111 #include "internal/cryptlib.h"
112 #include "internal/constant_time_locl.h"
119 # define alloca _alloca
121 #elif defined(__GNUC__)
123 # define alloca(s) __builtin_alloca((s))
129 #include "rsaz_exp.h"
132 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
133 # include "sparc_arch.h"
134 extern unsigned int OPENSSL_sparcv9cap_P[];
135 # define SPARC_T4_MONT
138 /* maximum precomputation table size for *variable* sliding windows */
139 #define TABLE_SIZE 32
141 /* this one works - simple but works */
142 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
144 int i, bits, ret = 0;
147 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
148 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
149 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
154 if ((r == a) || (r == p))
155 rr = BN_CTX_get(ctx);
159 if (rr == NULL || v == NULL)
162 if (BN_copy(v, a) == NULL)
164 bits = BN_num_bits(p);
167 if (BN_copy(rr, a) == NULL)
174 for (i = 1; i < bits; i++) {
175 if (!BN_sqr(v, v, ctx))
177 if (BN_is_bit_set(p, i)) {
178 if (!BN_mul(rr, rr, v, ctx))
191 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
201 * For even modulus m = 2^k*m_odd, it might make sense to compute
202 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
203 * exponentiation for the odd part), using appropriate exponent
204 * reductions, and combine the results using the CRT.
206 * For now, we use Montgomery only if the modulus is odd; otherwise,
207 * exponentiation using the reciprocal-based quick remaindering
210 * (Timing obtained with expspeed.c [computations a^p mod m
211 * where a, p, m are of the same length: 256, 512, 1024, 2048,
212 * 4096, 8192 bits], compared to the running time of the
213 * standard algorithm:
215 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
216 * 55 .. 77 % [UltraSparc processor, but
217 * debug-solaris-sparcv8-gcc conf.]
219 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
220 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
222 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
223 * at 2048 and more bits, but at 512 and 1024 bits, it was
224 * slower even than the standard algorithm!
226 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
227 * should be obtained when the new Montgomery reduction code
228 * has been integrated into OpenSSL.)
232 #define MONT_EXP_WORD
237 * I have finally been able to take out this pre-condition of the top bit
238 * being set. It was caused by an error in BN_div with negatives. There
239 * was also another problem when for a^b%m a >= m. eay 07-May-97
241 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
244 # ifdef MONT_EXP_WORD
245 if (a->top == 1 && !a->neg
246 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
247 BN_ULONG A = a->d[0];
248 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
251 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
256 ret = BN_mod_exp_recp(r, a, p, m, ctx);
260 ret = BN_mod_exp_simple(r, a, p, m, ctx);
268 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
269 const BIGNUM *m, BN_CTX *ctx)
271 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
274 /* Table of variables obtained from 'ctx' */
275 BIGNUM *val[TABLE_SIZE];
278 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
279 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
280 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
284 bits = BN_num_bits(p);
286 /* x**0 mod 1 is still zero. */
297 aa = BN_CTX_get(ctx);
298 val[0] = BN_CTX_get(ctx);
302 BN_RECP_CTX_init(&recp);
304 /* ignore sign of 'm' */
308 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
311 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
315 if (!BN_nnmod(val[0], a, m, ctx))
317 if (BN_is_zero(val[0])) {
323 window = BN_window_bits_for_exponent_size(bits);
325 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
327 j = 1 << (window - 1);
328 for (i = 1; i < j; i++) {
329 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
330 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
335 start = 1; /* This is used to avoid multiplication etc
336 * when there is only the value '1' in the
338 wvalue = 0; /* The 'value' of the window */
339 wstart = bits - 1; /* The top bit of the window */
340 wend = 0; /* The bottom bit of the window */
346 if (BN_is_bit_set(p, wstart) == 0) {
348 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
356 * We now have wstart on a 'set' bit, we now need to work out how bit
357 * a window to do. To do this we need to scan forward until the last
358 * set bit before the end of the window
363 for (i = 1; i < window; i++) {
366 if (BN_is_bit_set(p, wstart - i)) {
367 wvalue <<= (i - wend);
373 /* wend is the size of the current window */
375 /* add the 'bytes above' */
377 for (i = 0; i < j; i++) {
378 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
382 /* wvalue will be an odd number < 2^window */
383 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
386 /* move the 'window' down further */
396 BN_RECP_CTX_free(&recp);
401 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
402 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
404 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
408 /* Table of variables obtained from 'ctx' */
409 BIGNUM *val[TABLE_SIZE];
410 BN_MONT_CTX *mont = NULL;
412 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
413 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
421 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
424 bits = BN_num_bits(p);
426 /* x**0 mod 1 is still zero. */
439 val[0] = BN_CTX_get(ctx);
440 if (!d || !r || !val[0])
444 * If this is not done, things will break in the montgomery part
450 if ((mont = BN_MONT_CTX_new()) == NULL)
452 if (!BN_MONT_CTX_set(mont, m, ctx))
456 if (a->neg || BN_ucmp(a, m) >= 0) {
457 if (!BN_nnmod(val[0], a, m, ctx))
462 if (BN_is_zero(aa)) {
467 if (!BN_to_montgomery(val[0], aa, mont, ctx))
470 window = BN_window_bits_for_exponent_size(bits);
472 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
474 j = 1 << (window - 1);
475 for (i = 1; i < j; i++) {
476 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
477 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
482 start = 1; /* This is used to avoid multiplication etc
483 * when there is only the value '1' in the
485 wvalue = 0; /* The 'value' of the window */
486 wstart = bits - 1; /* The top bit of the window */
487 wend = 0; /* The bottom bit of the window */
489 #if 1 /* by Shay Gueron's suggestion */
490 j = m->top; /* borrow j */
491 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
492 if (bn_wexpand(r, j) == NULL)
494 /* 2^(top*BN_BITS2) - m */
495 r->d[0] = (0 - m->d[0]) & BN_MASK2;
496 for (i = 1; i < j; i++)
497 r->d[i] = (~m->d[i]) & BN_MASK2;
500 * Upper words will be zero if the corresponding words of 'm' were
501 * 0xfff[...], so decrement r->top accordingly.
506 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
509 if (BN_is_bit_set(p, wstart) == 0) {
511 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
520 * We now have wstart on a 'set' bit, we now need to work out how bit
521 * a window to do. To do this we need to scan forward until the last
522 * set bit before the end of the window
527 for (i = 1; i < window; i++) {
530 if (BN_is_bit_set(p, wstart - i)) {
531 wvalue <<= (i - wend);
537 /* wend is the size of the current window */
539 /* add the 'bytes above' */
541 for (i = 0; i < j; i++) {
542 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
546 /* wvalue will be an odd number < 2^window */
547 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
550 /* move the 'window' down further */
557 #if defined(SPARC_T4_MONT)
558 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
559 j = mont->N.top; /* borrow j */
560 val[0]->d[0] = 1; /* borrow val[0] */
561 for (i = 1; i < j; i++)
564 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
568 if (!BN_from_montgomery(rr, r, mont, ctx))
573 BN_MONT_CTX_free(mont);
579 #if defined(SPARC_T4_MONT)
580 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
585 wordpos = bitpos / BN_BITS2;
587 if (wordpos >= 0 && wordpos < a->top) {
588 ret = a->d[wordpos] & BN_MASK2;
591 if (++wordpos < a->top)
592 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
596 return ret & BN_MASK2;
601 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
602 * layout so that accessing any of these table values shows the same access
603 * pattern as far as cache lines are concerned. The following functions are
604 * used to transfer a BIGNUM from/to that table.
607 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
608 unsigned char *buf, int idx,
612 int width = 1 << window;
613 BN_ULONG *table = (BN_ULONG *)buf;
616 top = b->top; /* this works because 'buf' is explicitly
618 for (i = 0, j = idx; i < top; i++, j += width) {
625 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
626 unsigned char *buf, int idx,
630 int width = 1 << window;
631 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
633 if (bn_wexpand(b, top) == NULL)
637 for (i = 0; i < top; i++, table += width) {
640 for (j = 0; j < width; j++) {
642 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
648 int xstride = 1 << (window - 2);
649 BN_ULONG y0, y1, y2, y3;
651 i = idx >> (window - 2); /* equivalent of idx / xstride */
652 idx &= xstride - 1; /* equivalent of idx % xstride */
654 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
655 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
656 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
657 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
659 for (i = 0; i < top; i++, table += width) {
662 for (j = 0; j < xstride; j++) {
663 acc |= ( (table[j + 0 * xstride] & y0) |
664 (table[j + 1 * xstride] & y1) |
665 (table[j + 2 * xstride] & y2) |
666 (table[j + 3 * xstride] & y3) )
667 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
680 * Given a pointer value, compute the next address that is a cache line
683 #define MOD_EXP_CTIME_ALIGN(x_) \
684 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
687 * This variant of BN_mod_exp_mont() uses fixed windows and the special
688 * precomputation memory layout to limit data-dependency to a minimum to
689 * protect secret exponents (cf. the hyper-threading timing attacks pointed
690 * out by Colin Percival,
691 * http://www.daemonology.net/hyperthreading-considered-harmful/)
693 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
694 const BIGNUM *m, BN_CTX *ctx,
695 BN_MONT_CTX *in_mont)
697 int i, bits, ret = 0, window, wvalue;
699 BN_MONT_CTX *mont = NULL;
702 unsigned char *powerbufFree = NULL;
704 unsigned char *powerbuf = NULL;
706 #if defined(SPARC_T4_MONT)
715 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
721 bits = BN_num_bits(p);
723 /* x**0 mod 1 is still zero. */
736 * Allocate a montgomery context if it was not supplied by the caller. If
737 * this is not done, things will break in the montgomery part.
742 if ((mont = BN_MONT_CTX_new()) == NULL)
744 if (!BN_MONT_CTX_set(mont, m, ctx))
750 * If the size of the operands allow it, perform the optimized
751 * RSAZ exponentiation. For further information see
752 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
754 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
755 && rsaz_avx2_eligible()) {
756 if (NULL == bn_wexpand(rr, 16))
758 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
765 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
766 if (NULL == bn_wexpand(rr, 8))
768 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
777 /* Get the window size to use with size of p. */
778 window = BN_window_bits_for_ctime_exponent_size(bits);
779 #if defined(SPARC_T4_MONT)
780 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
781 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
782 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
786 #if defined(OPENSSL_BN_ASM_MONT5)
788 window = 5; /* ~5% improvement for RSA2048 sign, and even
790 /* reserve space for mont->N.d[] copy */
791 powerbufLen += top * sizeof(mont->N.d[0]);
797 * Allocate a buffer large enough to hold all of the pre-computed powers
798 * of am, am itself and tmp.
800 numPowers = 1 << window;
801 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
803 numPowers ? (2 * top) : numPowers));
805 if (powerbufLen < 3072)
807 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
811 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
815 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
816 memset(powerbuf, 0, powerbufLen);
819 if (powerbufLen < 3072)
823 /* lay down tmp and am right after powers table */
824 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
826 tmp.top = am.top = 0;
827 tmp.dmax = am.dmax = top;
828 tmp.neg = am.neg = 0;
829 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
831 /* prepare a^0 in Montgomery domain */
832 #if 1 /* by Shay Gueron's suggestion */
833 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
834 /* 2^(top*BN_BITS2) - m */
835 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
836 for (i = 1; i < top; i++)
837 tmp.d[i] = (~m->d[i]) & BN_MASK2;
841 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
844 /* prepare a^1 in Montgomery domain */
845 if (a->neg || BN_ucmp(a, m) >= 0) {
846 if (!BN_mod(&am, a, m, ctx))
848 if (!BN_to_montgomery(&am, &am, mont, ctx))
850 } else if (!BN_to_montgomery(&am, a, mont, ctx))
853 #if defined(SPARC_T4_MONT)
855 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
856 const BN_ULONG *n0, const void *table,
857 int power, int bits);
858 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
859 const BN_ULONG *n0, const void *table,
860 int power, int bits);
861 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
862 const BN_ULONG *n0, const void *table,
863 int power, int bits);
864 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
865 const BN_ULONG *n0, const void *table,
866 int power, int bits);
867 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
868 const BN_ULONG *n0, const void *table,
869 int power, int bits);
870 static const bn_pwr5_mont_f pwr5_funcs[4] = {
871 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
872 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
874 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
876 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
877 const void *bp, const BN_ULONG *np,
879 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
880 const BN_ULONG *np, const BN_ULONG *n0);
881 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
882 const void *bp, const BN_ULONG *np,
884 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
885 const void *bp, const BN_ULONG *np,
887 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
888 const void *bp, const BN_ULONG *np,
890 static const bn_mul_mont_f mul_funcs[4] = {
891 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
892 bn_mul_mont_t4_24, bn_mul_mont_t4_32
894 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
896 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
897 const void *bp, const BN_ULONG *np,
898 const BN_ULONG *n0, int num);
899 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
900 const void *bp, const BN_ULONG *np,
901 const BN_ULONG *n0, int num);
902 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
903 const void *table, const BN_ULONG *np,
904 const BN_ULONG *n0, int num, int power);
905 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
906 void *table, size_t power);
907 void bn_gather5_t4(BN_ULONG *out, size_t num,
908 void *table, size_t power);
909 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
911 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
912 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
916 * BN_to_montgomery can contaminate words above .top [in
917 * BN_DEBUG[_DEBUG] build]...
919 for (i = am.top; i < top; i++)
921 for (i = tmp.top; i < top; i++)
924 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
925 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
926 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
927 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
928 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
929 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
931 for (i = 3; i < 32; i++) {
932 /* Calculate a^i = a^(i-1) * a */
933 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
934 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
935 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
936 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
939 /* switch to 64-bit domain */
940 np = alloca(top * sizeof(BN_ULONG));
942 bn_flip_t4(np, mont->N.d, top);
945 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
946 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
947 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
950 * Scan the exponent one window at a time starting from the most
957 wvalue = bn_get_bits(p, bits + 1);
959 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
961 /* retry once and fall back */
962 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
966 wvalue >>= stride - 5;
968 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
969 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
970 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
971 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
972 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
973 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
977 bn_flip_t4(tmp.d, tmp.d, top);
979 /* back to 32-bit domain */
981 bn_correct_top(&tmp);
982 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
985 #if defined(OPENSSL_BN_ASM_MONT5)
986 if (window == 5 && top > 1) {
988 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
989 * specifically optimization of cache-timing attack countermeasures
990 * and pre-computation optimization.
994 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
995 * 512-bit RSA is hardly relevant, we omit it to spare size...
997 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
998 const void *table, const BN_ULONG *np,
999 const BN_ULONG *n0, int num, int power);
1000 void bn_scatter5(const BN_ULONG *inp, size_t num,
1001 void *table, size_t power);
1002 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
1003 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
1004 const void *table, const BN_ULONG *np,
1005 const BN_ULONG *n0, int num, int power);
1006 int bn_get_bits5(const BN_ULONG *ap, int off);
1007 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
1008 const BN_ULONG *not_used, const BN_ULONG *np,
1009 const BN_ULONG *n0, int num);
1011 BN_ULONG *n0 = mont->n0, *np;
1014 * BN_to_montgomery can contaminate words above .top [in
1015 * BN_DEBUG[_DEBUG] build]...
1017 for (i = am.top; i < top; i++)
1019 for (i = tmp.top; i < top; i++)
1023 * copy mont->N.d[] to improve cache locality
1025 for (np = am.d + top, i = 0; i < top; i++)
1026 np[i] = mont->N.d[i];
1028 bn_scatter5(tmp.d, top, powerbuf, 0);
1029 bn_scatter5(am.d, am.top, powerbuf, 1);
1030 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
1031 bn_scatter5(tmp.d, top, powerbuf, 2);
1034 for (i = 3; i < 32; i++) {
1035 /* Calculate a^i = a^(i-1) * a */
1036 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1037 bn_scatter5(tmp.d, top, powerbuf, i);
1040 /* same as above, but uses squaring for 1/2 of operations */
1041 for (i = 4; i < 32; i *= 2) {
1042 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1043 bn_scatter5(tmp.d, top, powerbuf, i);
1045 for (i = 3; i < 8; i += 2) {
1047 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1048 bn_scatter5(tmp.d, top, powerbuf, i);
1049 for (j = 2 * i; j < 32; j *= 2) {
1050 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1051 bn_scatter5(tmp.d, top, powerbuf, j);
1054 for (; i < 16; i += 2) {
1055 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1056 bn_scatter5(tmp.d, top, powerbuf, i);
1057 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1058 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1060 for (; i < 32; i += 2) {
1061 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1062 bn_scatter5(tmp.d, top, powerbuf, i);
1066 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1067 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1068 bn_gather5(tmp.d, top, powerbuf, wvalue);
1071 * Scan the exponent one window at a time starting from the most
1076 for (wvalue = 0, i = 0; i < 5; i++, bits--)
1077 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1079 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1080 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1081 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1082 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1083 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1084 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1088 wvalue = bn_get_bits5(p->d, bits - 4);
1090 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1094 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1096 bn_correct_top(&tmp);
1098 if (!BN_copy(rr, &tmp))
1100 goto err; /* non-zero ret means it's not error */
1105 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1107 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1111 * If the window size is greater than 1, then calculate
1112 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1113 * powers could instead be computed as (a^(i/2))^2 to use the slight
1114 * performance advantage of sqr over mul).
1117 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1119 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1122 for (i = 3; i < numPowers; i++) {
1123 /* Calculate a^i = a^(i-1) * a */
1124 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1126 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1133 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1134 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1135 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1140 * Scan the exponent one window at a time starting from the most
1144 wvalue = 0; /* The 'value' of the window */
1146 /* Scan the window, squaring the result as we go */
1147 for (i = 0; i < window; i++, bits--) {
1148 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1150 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1154 * Fetch the appropriate pre-computed value from the pre-buf
1156 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1160 /* Multiply the result into the intermediate result */
1161 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1166 /* Convert the final result from montgomery to standard format */
1167 #if defined(SPARC_T4_MONT)
1168 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1169 am.d[0] = 1; /* borrow am */
1170 for (i = 1; i < top; i++)
1172 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1176 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1180 if (in_mont == NULL)
1181 BN_MONT_CTX_free(mont);
1182 if (powerbuf != NULL) {
1183 OPENSSL_cleanse(powerbuf, powerbufLen);
1184 OPENSSL_free(powerbufFree);
1190 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1191 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1193 BN_MONT_CTX *mont = NULL;
1194 int b, bits, ret = 0;
1199 #define BN_MOD_MUL_WORD(r, w, m) \
1200 (BN_mul_word(r, (w)) && \
1201 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1202 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1204 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1205 * probably more overhead than always using BN_mod (which uses BN_copy if
1206 * a similar test returns true).
1209 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1210 * never negative (the result of BN_mod does not depend on the sign of
1213 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1214 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1216 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1217 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1218 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1225 if (!BN_is_odd(m)) {
1226 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1230 a %= m->d[0]; /* make sure that 'a' is reduced */
1232 bits = BN_num_bits(p);
1234 /* x**0 mod 1 is still zero. */
1250 d = BN_CTX_get(ctx);
1251 r = BN_CTX_get(ctx);
1252 t = BN_CTX_get(ctx);
1253 if (d == NULL || r == NULL || t == NULL)
1256 if (in_mont != NULL)
1259 if ((mont = BN_MONT_CTX_new()) == NULL)
1261 if (!BN_MONT_CTX_set(mont, m, ctx))
1265 r_is_one = 1; /* except for Montgomery factor */
1269 /* The result is accumulated in the product r*w. */
1270 w = a; /* bit 'bits-1' of 'p' is always set */
1271 for (b = bits - 2; b >= 0; b--) {
1272 /* First, square r*w. */
1274 if ((next_w / w) != w) { /* overflow */
1276 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1280 if (!BN_MOD_MUL_WORD(r, w, m))
1287 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1291 /* Second, multiply r*w by 'a' if exponent bit is set. */
1292 if (BN_is_bit_set(p, b)) {
1294 if ((next_w / a) != w) { /* overflow */
1296 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1300 if (!BN_MOD_MUL_WORD(r, w, m))
1309 /* Finally, set r:=r*w. */
1312 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1316 if (!BN_MOD_MUL_WORD(r, w, m))
1321 if (r_is_one) { /* can happen only if a == 1 */
1325 if (!BN_from_montgomery(rr, r, mont, ctx))
1330 if (in_mont == NULL)
1331 BN_MONT_CTX_free(mont);
1337 /* The old fallback, simple version :-) */
1338 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1339 const BIGNUM *m, BN_CTX *ctx)
1341 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1344 /* Table of variables obtained from 'ctx' */
1345 BIGNUM *val[TABLE_SIZE];
1347 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1348 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1349 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1353 bits = BN_num_bits(p);
1355 /* x**0 mod 1 is still zero. */
1366 d = BN_CTX_get(ctx);
1367 val[0] = BN_CTX_get(ctx);
1371 if (!BN_nnmod(val[0], a, m, ctx))
1373 if (BN_is_zero(val[0])) {
1379 window = BN_window_bits_for_exponent_size(bits);
1381 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1383 j = 1 << (window - 1);
1384 for (i = 1; i < j; i++) {
1385 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1386 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1391 start = 1; /* This is used to avoid multiplication etc
1392 * when there is only the value '1' in the
1394 wvalue = 0; /* The 'value' of the window */
1395 wstart = bits - 1; /* The top bit of the window */
1396 wend = 0; /* The bottom bit of the window */
1402 if (BN_is_bit_set(p, wstart) == 0) {
1404 if (!BN_mod_mul(r, r, r, m, ctx))
1412 * We now have wstart on a 'set' bit, we now need to work out how bit
1413 * a window to do. To do this we need to scan forward until the last
1414 * set bit before the end of the window
1419 for (i = 1; i < window; i++) {
1422 if (BN_is_bit_set(p, wstart - i)) {
1423 wvalue <<= (i - wend);
1429 /* wend is the size of the current window */
1431 /* add the 'bytes above' */
1433 for (i = 0; i < j; i++) {
1434 if (!BN_mod_mul(r, r, r, m, ctx))
1438 /* wvalue will be an odd number < 2^window */
1439 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1442 /* move the 'window' down further */